Distinguishing sets of strong recurrence from van der Corput sets

Abstract

AbstractSets of recurrence, which were introduced by Furstenberg, and van der Corput sets, which were introduced by Kamae and Mendés France, as well as variants thereof, are important classes of sets in Ergodic Theory. In this paper, we construct a set of strong recurrence which is not a van der Corput set. In particular, this shows that the class of enhanced van der Corput sets is a proper subclass of sets of strong recurrence. This answers some questions asked by Bergelson and Lesigne.